What is the role of inflation expectations in moveing from the short-run to the long-run?

Question

What is the role of inflation expectations in moveing from the short-run to the long-run?

Answer 1

Y=PQ

dY=dPQ+dQP

If we enter inflation dP/P

dY/P=dPQ/P+dQ

dP/P=dY/PQ-dQ/Q=1/Q[dY/P -dQ]

In the long run dQ/Q=0, inflation will obey to changes in the level of prices and

dP/P=dY/PQ

but in the long run

dY=0

and this means that

dP/P=0

So, inflation is zero in the long run.